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

下载

页码：888 / 907

页数：20

共 50 条

[1] On Weak Solutions of Stochastic Differential Equations
Hofmanova, Martina
Seidler, Jan
STOCHASTIC ANALYSIS AND APPLICATIONS, 2012, 30 (01) : 100 - 121
[2] On Weak Solutions of Stochastic Differential Equations II
Hofmanova, Martina
Seidler, Jan
STOCHASTIC ANALYSIS AND APPLICATIONS, 2013, 31 (04) : 663 - 670
[3] On weak solutions of backward stochastic differential equations
Buckdahn, R
Engelbert, HJ
Rascanu, A
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2004, 49 (01) : 16 - 50
[4] A NOTE ON THE WEAK-CONVERGENCE OF SOLUTIONS OF CERTAIN STOCHASTIC ORDINARY DIFFERENTIAL-EQUATIONS
WATANABE, H
LECTURE NOTES IN MATHEMATICS, 1983, 1021 : 690 - 698
[5] Predictability and uniqueness of weak solutions of the stochastic differential equations
Merkle, Ana
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2023, 31 (01): : 207 - 219
[6] On the continuity of weak solutions of backward stochastic differential equations
Buckdahn, R.
Engelbert, H. -J.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2008, 52 (01) : 152 - U14
[7] Weak solutions of stochastic differential equations with discontinuous coefficients
Levakov, AA
DIFFERENTIAL EQUATIONS, 2001, 37 (08) : 1088 - 1096
[8] Weak Solutions of Stochastic Differential Equations with Discontinuous Coefficients
A. A. Levakov
Differential Equations, 2001, 37 : 1088 - 1096
[9] ON WEAK SOLUTIONS OF STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS
METIVIER, M
VIOT, M
LECTURE NOTES IN MATHEMATICS, 1988, 1322 : 139 - 150
[10] NOTE ON STOCHASTIC DIFFERENTIAL-EQUATIONS WITH MARKOV SOLUTIONS
JACOD, J
PROTTER, P
LECTURE NOTES IN MATHEMATICS, 1991, 1485 : 138 - 139

← 1 2 3 4 5 →