**Proceedings of Symposia in Pure Mathematics**

Volume: 57;
1995;
621 pp;
Hardcover

MSC: Primary 34; 35; 58; 60; 82; 47; 81;

Print ISBN: 978-0-8218-0289-2

Product Code: PSPUM/57

List Price: $156.00

AMS Member Price: $124.80

MAA Member Price: $140.40

**Electronic ISBN: 978-0-8218-9359-3
Product Code: PSPUM/57.E**

List Price: $156.00

AMS Member Price: $124.80

MAA Member Price: $140.40

# Stochastic Analysis

Share this page *Edited by *
*Michael C. Cranston; Mark A. Pinsky*

This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Research Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.

#### Readership

Researchers in probability theory, partial differential equations, statistical mechanics, dynamical systems, and mathematical physics.

#### Reviews & Endorsements

This very rich volume … is an extremely valuable contribution to the literature on the interplay between stochastics and analysis. The editors have done a marvelous job in collecting a number of papers on subjects which in their entirety constitute the current activities in the field ... This volume has a particularly high standard and appears to be of special significance to current research activity in the ever-increasing field of stochastics and analysis.

-- Metrika, International Journal for Theoretical and Applied Statistics

# Table of Contents

## Stochastic Analysis

- Contents v6 free
- Preface ix10 free
- PART I: Problems in Analysis 112 free
- An improvement of the Osserman constant for the bass note of adrum 314
- Heat content asymptotics for some open sets with a fractal boundary 1122
- On self- attracting random walks 2334
- Positivity default for martingales and harmonic functions 4556
- Optimal switching between two Brownian motions 5364
- Nonnegative solutions for semilinear elliptic equations with boundaryconditions — a probabilistic approach 6576
- Simulated annealing and fastest cooling rates for some 1-dim spin glass models 8394
- Averaging stochastically perturbed Hamiltonian systems 93104
- The interpretation and solution of ordinary differential equationsdriven by rough signals 115126
- Time- reversal of the noisy Wiener- Hopf factorisation 129140
- Some aspects of Brownian motion in a Poissonian potential 137148
- Schrödinger operators and asymptotics for Poisson-Lévy excursionmeasures for one- dimensional time- homogeneous diffusions 145156
- Generalized arc-sine laws for one- dimensional diffusion processesand random walks 157168

- PART II: Problems in Geometry 173184
- Semimartingales with values in a Euclidean vector bundle and Ocone'sformula on a Riemannian manifold 175186
- Coupling constructions for hypoelliptic diffusions: Two examples 193204
- Heat kernel bounds on Riemannian manifolds 213224
- Brownian motion and harmonic functions on polygonal complexes 227238
- Heat kernel of a noncompact Riemannian manifold 239250
- Flows and quasi- invariance of the Wiener measure on path spaces 265276
- Levy's stochastic area formula and related problems 281292
- Markov processes and harmonic functions on hyperbolic metricspaces 307318
- Some problems concerning Lévy processes on Lie groups 323334
- The central limit theorem for geodesic flows on noncompact manifoldsof constant negative curvature 343354
- A renewal theorem for the distance in negative curvature 351362
- A bootstrap proof of the limit theorem for linear 361372
- Diffusion processes on a Lipschitz Riemannian manifold and theirapplications 373384

- PART III: Infinite-Dimensional Problems 383394
- On path properties of super- 2 processes. II 385396
- Towards calculus and geometry on path spaces 405416
- Branching with a single point catalyst 423434
- The Brownian path- valued process and its connections with partialdifferential equations 427438
- Inverse powers of white noise 439450
- Statistical mechanics of nonlinear wave equations 457468
- Markov properties for solutions of stochastic differential equations 465476
- A quasihomeomorphism on the Wiener space 473484
- Absolute continuity on the Wiener space and some applications 487498
- Invariant Gibbsian measures of the Klein- Gordon equation 495506

- PART IV: Stochastic PDE/Stochastic Flows 511522
- Dirichlet form methods for uniqueness of martingale problems and applications 513524
- Anticipative problems in the theory of random dynamical systems 529540
- Stability index for nonlinear stochastic differential equations 543554
- Degenerate stochastic differential equations, flows, and hypoellipticity 553564
- Derivative flows of stochastic differential equations: Moment exponentsand geometric properties 565576
- Invariant diffusion processes in Lie groups and stochastic flows 575586
- On stochastic integrals in topological vector spaces 593604
- Travelling waves for the KPP equation with noise 603614
- Backward SDEs, quasilinear PDEs, and SPDEs 611622
- Invariance of the Lyapunov exponent under nonlinear perturbations 619630