Estimates for exit time from an interval of length 2r before a prescribed time T are derived for solutions of a class of stochastic partial differential equations used to characterize two population models: super-Brownian motion and Fleming-Viot Process. These types of estimates are then derived for the two population models. The corresponding large deviation results are also applied for the acquired bounds.
{"title":"Some Exit Time Estimates for Super-Brownian Motion and Fleming-Viot Process","authors":"Parisa Fatheddin","doi":"10.31390/josa.1.2.02","DOIUrl":"https://doi.org/10.31390/josa.1.2.02","url":null,"abstract":"Estimates for exit time from an interval of length 2r before a prescribed time T are derived for solutions of a class of stochastic partial differential equations used to characterize two population models: super-Brownian motion and Fleming-Viot Process. These types of estimates are then derived for the two population models. The corresponding large deviation results are also applied for the acquired bounds.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129895964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Ogawa stochastic integral is shortly reviewed and formulated in the framework of abstract Wiener spaces. The condition of universal Ogawa integrability in the multidimensional case is investigated, proving that it cannot hold in general without the introduction of a "renormalization term". Explicit examples are provided.
{"title":"Ogawa Integrability and a Condition for Convergence in the Multidimensional Case","authors":"N. Cangiotti, S. Mazzucchi","doi":"10.31390/josa.1.1.04","DOIUrl":"https://doi.org/10.31390/josa.1.1.04","url":null,"abstract":"The Ogawa stochastic integral is shortly reviewed and formulated in the framework of abstract Wiener spaces. The condition of universal Ogawa integrability in the multidimensional case is investigated, proving that it cannot hold in general without the introduction of a \"renormalization term\". Explicit examples are provided.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130559986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Hessian of the fundamental solution to the parabolic problem for weighted Schr"odinger operators of the form $frac 12 Delta+nabla h-V$ proving a second order Feynman-Kac formula and obtaining Hessian estimates. For manifolds with a pole, we use the Jacobian determinant of the exponential map to offset the volume growth of the Riemannian measure and use the semi-classical bridge as a delta measure at $y_0$ to obtain exact Gaussian estimates. These estimates are in terms of bounds on $Ric-2 Hess (h)$, on the curvature operator, and on the cyclic sum of the gradient of the Ricci tensor.
{"title":"Hessian Formulas and Estimates for Parabolic Schrödinger Operators","authors":"Xue-Mei Li","doi":"10.31390/josa.2.3.07","DOIUrl":"https://doi.org/10.31390/josa.2.3.07","url":null,"abstract":"We study the Hessian of the fundamental solution to the parabolic problem for weighted Schr\"odinger operators of the form $frac 12 Delta+nabla h-V$ proving a second order Feynman-Kac formula and obtaining Hessian estimates. For manifolds with a pole, we use the Jacobian determinant of the exponential map to offset the volume growth of the Riemannian measure and use the semi-classical bridge as a delta measure at $y_0$ to obtain exact Gaussian estimates. \u0000These estimates are in terms of bounds on $Ric-2 Hess (h)$, on the curvature operator, and on the cyclic sum of the gradient of the Ricci tensor.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133930911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Taylor expansion for the solutions of differential equations driven by $p$-rough paths with $p>2$. We prove a general theorem concerning the convergence of the Taylor expansion on a nonempty interval provided that the vector fields are analytic on a ball centered at the initial point. We also derive criteria that enable us to study the rate of convergence of the Taylor expansion. Finally and this is also the main and the most original part of this paper, we prove Castell expansions and tail estimates with exponential decays for the remainder terms of the solutions of the stochastic differential equations driven by continuous centered Gaussian process with finite $2D~rho-$variation and fractional Brownian motion with Hurst parameter $H>1/4$.
{"title":"Taylor Expansions and Castell Estimates for Solutions of Stochastic Differential Equations Driven by Rough Paths","authors":"Qi Feng, Xuejing Zhang","doi":"10.31390/josa.1.2.04","DOIUrl":"https://doi.org/10.31390/josa.1.2.04","url":null,"abstract":"We study the Taylor expansion for the solutions of differential equations driven by $p$-rough paths with $p>2$. We prove a general theorem concerning the convergence of the Taylor expansion on a nonempty interval provided that the vector fields are analytic on a ball centered at the initial point. We also derive criteria that enable us to study the rate of convergence of the Taylor expansion. Finally and this is also the main and the most original part of this paper, we prove Castell expansions and tail estimates with exponential decays for the remainder terms of the solutions of the stochastic differential equations driven by continuous centered Gaussian process with finite $2D~rho-$variation and fractional Brownian motion with Hurst parameter $H>1/4$.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115879926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic differential equations with adapted integrands and initial conditions are well studied within Itô’s theory. However, such a general theory is not known for corresponding equations with anticipation. We use examples to illustrate essential ideas of the Ayed–Kuo integral and techniques for dealing with anticipating stochastic differential equations. We prove the general form of the solution for a class of linear stochastic differential equations with adapted coefficients and anticipating initial condition, which in this case is an analytic function of a Wiener integral. We show that for such equations, the conditional expectation of the solution is not the same as the solution of the corresponding stochastic differential equation with the initial condition as the expectation of the original initial condition. In particular, we show that there is an extra term in the stochastic differential equation, and give the exact form of this term.
{"title":"Anticipating Linear Stochastic Differential Equations with Adapted Coefficients","authors":"H. Kuo, Pujan Shrestha, S. Sinha","doi":"10.31390/josa.2.2.05","DOIUrl":"https://doi.org/10.31390/josa.2.2.05","url":null,"abstract":"Stochastic differential equations with adapted integrands and initial conditions are well studied within Itô’s theory. However, such a general theory is not known for corresponding equations with anticipation. We use examples to illustrate essential ideas of the Ayed–Kuo integral and techniques for dealing with anticipating stochastic differential equations. We prove the general form of the solution for a class of linear stochastic differential equations with adapted coefficients and anticipating initial condition, which in this case is an analytic function of a Wiener integral. We show that for such equations, the conditional expectation of the solution is not the same as the solution of the corresponding stochastic differential equation with the initial condition as the expectation of the original initial condition. In particular, we show that there is an extra term in the stochastic differential equation, and give the exact form of this term.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129773692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：