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Persistent random walk

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226: 101: 126: 55: 121: 299: 57:, and each particle's velocity may be reversed at any moment. The reversal time is exponentially distributed as 294: 60: 250: 229: 33: 8: 106: 266: 270: 221:{\displaystyle (2\tau ^{-1}\partial _{t}+\partial _{tt}-c_{0}^{2}\partial _{xx})n=0} 262: 288: 274: 251:"Some applications of persistent random walks and the telegrapher's equation" 30:
A population of particles are distributed on a line, with constant speed
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Physica A: Statistical Mechanics and its Applications
129: 109: 63: 36: 220: 115: 95: 49: 286: 287: 248: 16:Modification of the random walk model 13: 194: 163: 150: 96:{\displaystyle e^{-t/\tau }/\tau } 14: 311: 242: 249:Weiss, George H (2002-08-15). 206: 130: 103:, then the population density 1: 267:10.1016/S0378-4371(02)00805-1 235: 7: 10: 316: 23:is a modification of the 300:Variants of random walks 230:telegrapher's equation 222: 117: 97: 51: 21:persistent random walk 223: 118: 98: 52: 50:{\displaystyle c_{0}} 295:Stochastic processes 127: 123:evolves according to 107: 61: 34: 192: 218: 178: 113: 93: 47: 116:{\displaystyle n} 307: 279: 278: 246: 227: 225: 224: 219: 205: 204: 191: 186: 174: 173: 158: 157: 148: 147: 122: 120: 119: 114: 102: 100: 99: 94: 89: 84: 83: 79: 56: 54: 53: 48: 46: 45: 315: 314: 310: 309: 308: 306: 305: 304: 285: 284: 283: 282: 247: 243: 238: 197: 193: 187: 182: 166: 162: 153: 149: 140: 136: 128: 125: 124: 108: 105: 104: 85: 75: 68: 64: 62: 59: 58: 41: 37: 35: 32: 31: 17: 12: 11: 5: 313: 303: 302: 297: 281: 280: 261:(3): 381–410. 240: 239: 237: 234: 217: 214: 211: 208: 203: 200: 196: 190: 185: 181: 177: 172: 169: 165: 161: 156: 152: 146: 143: 139: 135: 132: 112: 92: 88: 82: 78: 74: 71: 67: 44: 40: 15: 9: 6: 4: 3: 2: 312: 301: 298: 296: 293: 292: 290: 276: 272: 268: 264: 260: 256: 252: 245: 241: 233: 231: 228:which is the 215: 212: 209: 201: 198: 188: 183: 179: 175: 170: 167: 159: 154: 144: 141: 137: 133: 110: 90: 86: 80: 76: 72: 69: 65: 42: 38: 28: 26: 22: 258: 254: 244: 29: 20: 18: 25:random walk 289:Categories 236:References 275:0378-4371 195:∂ 176:− 164:∂ 151:∂ 142:− 138:τ 91:τ 81:τ 70:− 27:model. 273:  271:ISSN 19:The 263:doi 259:311 291:: 269:. 257:. 253:. 232:. 277:. 265:: 216:0 213:= 210:n 207:) 202:x 199:x 189:2 184:0 180:c 171:t 168:t 160:+ 155:t 145:1 134:2 131:( 111:n 87:/ 77:/ 73:t 66:e 43:0 39:c

Index

random walk
telegrapher's equation
"Some applications of persistent random walks and the telegrapher's equation"
doi
10.1016/S0378-4371(02)00805-1
ISSN
0378-4371
Categories
Stochastic processes
Variants of random walks

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