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Further properties on functional SDEs. / Jianhai Bao

Swansea University Author: Jianhai Bao

Abstract

In this work, we aim to study some fine properties for functional stochastic differential equation. The results consist of five main parts. In the second chapter, by constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigro...

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Published: 2013
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42334
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first_indexed 2018-08-02T18:54:27Z
last_indexed 2018-08-03T10:09:52Z
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spelling 2018-08-02T16:24:28.8697888 v2 42334 2018-08-02 Further properties on functional SDEs. 3501a546f6cb5fc0dbf643d49e64cef7 NULL Jianhai Bao Jianhai Bao true true 2018-08-02 In this work, we aim to study some fine properties for functional stochastic differential equation. The results consist of five main parts. In the second chapter, by constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigroup associated with a class of degenerate functional stochastic differential equations. In the third chapter, by using Malliavin calculus, explicit derivative formulae are established for a class of semi-linear functional stochastic partial differential equations with additive or multiplicative noise. As applications, gradient estimates and Harnack inequalities are derived for the semigroup of the associated segment process. In the fourth chapter, we apply the weak convergence approach to establish a large deviation principle for a class of neutral functional stochastic differential equations with jumps. In particular, we discuss the large deviation principle for neutral stochastic differential delay equations which allow the coefficients to be highly nonlinear with respect to the delay argument. In the fifth chapter, we discuss the convergence of Euler-Maruyama scheme for a class of neutral stochastic partial differential equations driven by alpha-stable processes, where the numerical scheme is based on spatial discretization and time discretization. In the last chapter, we discuss (i) the existence and uniqueness of the stationary distribution of explicit Euler-Maruyama scheme both in time and in space for a class of stochastic partial differential equations whenever the stepsize is sufficiently small, and (ii) show that the stationary distribution of the Euler-Maruyama scheme converges weakly to the counterpart of the stochastic partial differential equation. E-Thesis Mathematics. 31 12 2013 2013-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:28.8697888 2018-08-02T16:24:28.8697888 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jianhai Bao NULL 1 0042334-02082018162446.pdf 10798042.pdf 2018-08-02T16:24:46.2630000 Output 3772574 application/pdf E-Thesis true 2018-08-02T16:24:46.2630000 false
title Further properties on functional SDEs.
spellingShingle Further properties on functional SDEs.
Jianhai Bao
title_short Further properties on functional SDEs.
title_full Further properties on functional SDEs.
title_fullStr Further properties on functional SDEs.
title_full_unstemmed Further properties on functional SDEs.
title_sort Further properties on functional SDEs.
author_id_str_mv 3501a546f6cb5fc0dbf643d49e64cef7
author_id_fullname_str_mv 3501a546f6cb5fc0dbf643d49e64cef7_***_Jianhai Bao
author Jianhai Bao
author2 Jianhai Bao
format E-Thesis
publishDate 2013
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description In this work, we aim to study some fine properties for functional stochastic differential equation. The results consist of five main parts. In the second chapter, by constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigroup associated with a class of degenerate functional stochastic differential equations. In the third chapter, by using Malliavin calculus, explicit derivative formulae are established for a class of semi-linear functional stochastic partial differential equations with additive or multiplicative noise. As applications, gradient estimates and Harnack inequalities are derived for the semigroup of the associated segment process. In the fourth chapter, we apply the weak convergence approach to establish a large deviation principle for a class of neutral functional stochastic differential equations with jumps. In particular, we discuss the large deviation principle for neutral stochastic differential delay equations which allow the coefficients to be highly nonlinear with respect to the delay argument. In the fifth chapter, we discuss the convergence of Euler-Maruyama scheme for a class of neutral stochastic partial differential equations driven by alpha-stable processes, where the numerical scheme is based on spatial discretization and time discretization. In the last chapter, we discuss (i) the existence and uniqueness of the stationary distribution of explicit Euler-Maruyama scheme both in time and in space for a class of stochastic partial differential equations whenever the stepsize is sufficiently small, and (ii) show that the stationary distribution of the Euler-Maruyama scheme converges weakly to the counterpart of the stochastic partial differential equation.
published_date 2013-12-31T03:52:45Z
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score 11.016593

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