A NOTE ON WEAK SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS

被引：4

作者：

Ondrejat, Martin ^{[1
]}

Seidler, Jan ^{[1
]}

机构：

[1] Czech Acad Sci, Inst Informat Theory & Automat, Vodarenskou Vezi 4, Prague 18208 8, Czech Republic

来源：

KYBERNETIKA | 2018年 / 54卷 / 05期

关键词：

stochastic differential equations; continuous coefficients; weak solutions;

D O I：

10.14736/kyb-2018-5-0888

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.

引用

收藏

页码：888 / 907

页数：20

相关论文

共 17 条

[1] STOCHASTIC NAVIER-STOKES EQUATIONS [J].

BENSOUSSAN, A .

ACTA APPLICANDAE MATHEMATICAE, 1995, 38 (03) :267-304

[2]

Billingsley P., 1968, CONVERGE PROBAB MEAS, DOI [DOI 10.1002/9780470316962, 10.1002/9780470316962]

[3]

Bogachev V.I., 2007, MEASURE THEORY, V1, DOI 10.1007/978-3-540-34514-5

[4] Invariant measures for stochastic nonlinear beam and wave equations [J].

Brzezniak, Zdzislaw ;

Ondrejat, Martin ;

Seidler, Jan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (05) :4157-4179

[5] Some particular problems of martingale theory [J].

Cherny, A .

From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, :109-124

[6] Local martingale and pathwise solutions for an abstract fluids model [J].

Debussche, Arnaud ;

Glatt-Holtz, Nathan ;

Temam, Roger .

PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (14-15) :1123-1144

[7]

Dudley R. M., 2002, Cambridge Studies in Advanced Mathematics, V2nd, DOI [10.1017/CBO9780511755347, DOI 10.1017/CBO9780511755347]

[8]

Gyongy I, 1996, PROBAB THEORY REL, V105, P143

[9] On Weak Solutions of Stochastic Differential Equations II [J].

Hofmanova, Martina ;

Seidler, Jan .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2013, 31 (04) :663-670

[10] On Weak Solutions of Stochastic Differential Equations [J].

Hofmanova, Martina ;

Seidler, Jan .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2012, 30 (01) :100-121