{
  "aliases": null,
  "backlinks": [
    {
      "field": "specializes",
      "target": "22735FGJV6"
    },
    {
      "field": "defines",
      "target": "CP7Q2FWWNT"
    },
    {
      "field": "about",
      "target": "Q82B4H4Z4J"
    },
    {
      "field": "uses",
      "target": "Q82B4H4Z4J"
    }
  ],
  "body": "\n## Summary\n\nA Lévy process is a stochastic process that starts at $0$ and has independent and stationary increments, with paths continuous in probability.\nIt is the continuous-time analogue of a random walk.\nBrownian motion and the Poisson process are the two basic examples, and every Lévy process combines a drift, a Brownian part and jumps.\nThe law of each $X_t$ is [[infinitely divisible|BX3V3NYM1Y]], and the [[Lévy–Khintchine representation|Q82B4H4Z4J]] describes all of them.\n\n## Explanations\n\n### L1 human\n\nA Lévy process moves by random increments that do not remember the past and do not depend on the clock.\nWhat happens between time $1$ and time $2$ has the same law as what happens between time $5$ and time $6$, and the two pieces are independent.\nThe path may move continuously, like Brownian motion, or jump, like a counter of random clicks.\nFor example, the number of radioactive decays up to time $t$ is a Poisson process, a Lévy process that jumps by $1$.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "60G51",
      "60J25"
    ],
    "name": "Lévy process",
    "same_as": {
      "wikidata": "Q1557613",
      "wikipedia": "Lévy process"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Lévy_process"
      }
    ],
    "specializes": [
      "0QH5ENKZM1"
    ],
    "tag": "8NT5CFG2ZR"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/8NT5CFG2ZR/",
  "links": [
    {
      "field": "specializes",
      "target": "0QH5ENKZM1"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/8NT5CFG2ZR.md",
  "msc": [
    "60G51",
    "60J25"
  ],
  "name": "Lévy process",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/8NT/8NT5CFG2ZR.md",
  "status": null,
  "tag": "8NT5CFG2ZR",
  "uri": "m2://8NT5CFG2ZR",
  "url": "https://math2.tamnd.com/wiki/levy-process/",
  "writing": {
    "tag": "8NT5CFG2ZR",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}