| Introduction | p. 1 |
| Gaussian diffusions | |
| Gaussian diffusion. Probabilistic and analytic approaches | p. 17 |
| Classification of Gaussian diffusions by the Young schemes | p. 20 |
| Longtime behaviourofthe Greenfunctions ofGaussiandiffusions | p. 25 |
| Complex stochastic Gaussian diffusion | p. 28 |
| The rate of escape for Gaussian diffusions and scattering for its perturbations | p. 34 |
| Boundary value problem for Hamiltonian systems | |
| Rapid course in calculus of variations | p. 40 |
| Boundary value problem for non-degenerate Hamiltonians | p. 50 |
| RegulardegenerateHamiltoniansofthe firstrank | p. 59 |
| General regular Hamiltonians depending quadratically on momenta | p. 72 |
| Hamiltonians of exponential growth in momenta | p. 75 |
| Complex Hamiltonians and calculus of variations of saddle-points | p. 87 |
| Stochastic Hamiltonians | p. 92 |
| Semiclassical approximation for regular diffusion | |
| Main ideas of the WKB-method with imaginary phase | p. 97 |
| Calculation of the two-point function for regular Hamiltonians | p. 104 |
| Asymptotic solutionsofthe transportequation | p. 110 |
| Local asymptotics of the Green function for regular Hamiltonians | p. 112 |
| Global small diffusion asymptotics and large deviations | p. 119 |
| Asymptotics for non-regular diffusion: an example | p. 124 |
| Analytic solutions to some linear PDE | p. 128 |
| Invariant degenerate diffusion on cotangent bundles | |
| Curvilinear Ornstein-Uhlenbeck process and stochastic geodesic flow | p. 136 |
| Small time asymptotics for stochastic geodesic flow | p. 140 |
| The traceofthe Greenfunctionandgeometricinvariants | p. 143 |
| Transition probability densities for stable jump-diffusion | |
| Asymptotic properties of one-dimensional stable laws | p. 146 |
| Asymptotic properties of finite-dimensional stable laws | p. 149 |
| Transition probability densities for stable jump-diffusion | p. 161 |
| Stable jump-diffusions combined with compound Poisson processes | p. 178 |
| Stable-like processes | p. 182 |
| Applications to the sample path properties of stable jump-diffusions | p. 187 |
| Semiclassical asymptotics for the localised Feller-Courrege processes | |
| Maslov's tunnel equations and the Feller-Courrege processes | p. 191 |
| Rough local asymptotics and local large deviations | p. 194 |
| Refinementandglobalisation | p. 217 |
| Complex stochastic diffusions or stochastic Schrodinger equations | |
| Semiclassical approximation: formal asymptotics | p. 223 |
| Semiclassical approximation: justification and globalisation | p. 229 |
| Applications: two-sided estimates to complex heat kernels, large deviation principle, well-posedness of the Cauchy problem | p. 235 |
| Path integration and infinite-dimensional saddle-point method | p. 236 |
| Some topics in Semiclassical spectral analysis | |
| Double-well splitting | p. 239 |
| Low lying eigenvalues of diffusion operators and the life-times of diffusion processes | p. 247 |
| Quasi-modes of diffusion operators around a closed orbit of the corresponding classical system | p. 252 |
| Path integration for the Schrodinger, heat and complex stochastic diffusion equations | |
| Introduction | p. 255 |
| Path integral for the Schrodinger equation in p-representation | p. 263 |
| Path integral for the Schrodinger equation in x-representation | p. 267 |
| Singular potentials | p. 269 |
| Semiclassical asymptotics | p. 272 |
| Fock space representation | p. 276 |
| Appendices | |
| Main equation of the theory of continuous quantum measurements | p. 280 |
| Asymptotics of Laplace integrals with complex phase | p. 283 |
| Characteristic functions of stable laws | p. 293 |
| Levy-Khintchine ?DO and Feller-Courrege processes | p. 298 |
| Equivalence of convex functions | p. 303 |
| Unimodality of symmetric stable laws | p. 305 |
| Infinite divisible complex distributions and complex Markov processes | p. 312 |
| A review of main approaches to the rigorous construction of path integral | p. 322 |
| Perspectives and problems | p. 326 |
| References | p. 329 |
| Main notations | p. 346 |
| Subject Index | p. 347 |
| Table of Contents provided by Publisher. All Rights Reserved. |
