03069nam 2200589 450 991081365210332120170822144323.01-4704-0218-1(CKB)3360000000464813(EBL)3114373(SSID)ssj0000889211(PQKBManifestationID)11478759(PQKBTitleCode)TC0000889211(PQKBWorkID)10876022(PQKB)10457235(MiAaPQ)EBC3114373(RPAM)1655616(PPN)195415132(EXLCZ)99336000000046481319971112d1998 uy| 0engur|n|---|||||txtccrShort-time geometry of random heat kernels /Richard B. SowersProvidence, Rhode Island :American Mathematical Society,1998.1 online resource (145 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 629"March 1998, volume 132, number 629 (end of volume)."0-8218-0649-1 Includes bibliographical references.""Contents""; ""Chapter 1. Introduction""; ""Â1.1. The Short-Time Problem""; ""Â1.2. The Main Results and Some Examples""; ""Â1.3. Notation and Assumptions""; ""Chapter 2. Guessing the Dominant Asymptotics""; ""Â2.1. A Simpler Problem""; ""Â2.2. A Minimization Problem""; ""Â2.3. A Rate Function and Approximation for the Random Heat Kernel""; ""Â2.4. Representation Results for the Secondary and Tertiary Terms""; ""Chapter 3. Initial Condition and Evolution of the Approximate Kernel""; ""Â3.1. The Short-Time Behavior of the Approximation""; ""Â3.2. The Evolution of the Approximation""""Chapter 4. The Minakshisundaram-Pleijel Coefficients""""Â4.1. An Ansatz""; ""Â4.2. Some Results on Multiple Wiener Integrals""; ""Â4.3. The Minakshisundaram-Pleijel Expansion""; ""Chapter 5. Error Estimates, Proof of the Main Theorem, and Extensions""; ""Â5.1. Setup of Equations""; ""Â5.2. Estimates on the Continuity of SPDE's""; ""Â5.3. The Near-Field Error""; ""Â5.4. The Far-Field Error""; ""Â5.5. Proof of the Main Theorem""; ""Â5.6. Extensions""; ""Appendices""; ""Appendix A: The Jacobi Flow""; ""Appendix B: Some Results on Multiple Wiener Integrals""""Appendix C: Garsia-Rodemich-Rumsey Estimates""""Bibliography""Memoirs of the American Mathematical Society ;no. 629.Heat equationStochastic partial differential equationsFilters (Mathematics)Heat equation.Stochastic partial differential equations.Filters (Mathematics)510 s519.2Sowers R. B(Richard Bucher),1965-1706315MiAaPQMiAaPQMiAaPQBOOK9910813652103321Short-time geometry of random heat kernels4093644UNINA